Expanding the Class of Quadratic Control-Lyapunov Functions for Low-Thrust Trajectory Optimization
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866929479131070464 |
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| author | Nurre, Nicholas P. Tafazzol, Saeid Taheri, Ehsan |
| author_facet | Nurre, Nicholas P. Tafazzol, Saeid Taheri, Ehsan |
| contents | Control laws derived from Control-Lyapunov Functions (CLFs) offer an efficient way for generating near-optimal many-revolution low-thrust trajectories. A common approach to constructing CLFs is to consider the family of quadratic functions using a diagonal weighting matrix. In this paper, we explore the advantages of using a larger family of quadratic functions. More specifically, we consider positive-definite weighting matrices with non-zero off-diagonal elements (hereafter referred to as "full" matrices). We propose a novel eigendecomposition method for parameterizing $N$-dimensional weighting matrices that is easy to implement and guarantees positive-definiteness of the weighting matrices. We use particle swarm optimization, which is a stochastic optimization algorithm, to optimize the parameters and generate near-optimal minimum-time low-thrust trajectories. Solutions obtained using a full positive-definite matrix are compared to the results from the (standard) diagonal weighting matrix for a number of benchmark problems. Results demonstrate that improvements in optimality are achieved, especially for maneuvers with large changes in orbital elements. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_14412 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Expanding the Class of Quadratic Control-Lyapunov Functions for Low-Thrust Trajectory Optimization Nurre, Nicholas P. Tafazzol, Saeid Taheri, Ehsan Optimization and Control Control laws derived from Control-Lyapunov Functions (CLFs) offer an efficient way for generating near-optimal many-revolution low-thrust trajectories. A common approach to constructing CLFs is to consider the family of quadratic functions using a diagonal weighting matrix. In this paper, we explore the advantages of using a larger family of quadratic functions. More specifically, we consider positive-definite weighting matrices with non-zero off-diagonal elements (hereafter referred to as "full" matrices). We propose a novel eigendecomposition method for parameterizing $N$-dimensional weighting matrices that is easy to implement and guarantees positive-definiteness of the weighting matrices. We use particle swarm optimization, which is a stochastic optimization algorithm, to optimize the parameters and generate near-optimal minimum-time low-thrust trajectories. Solutions obtained using a full positive-definite matrix are compared to the results from the (standard) diagonal weighting matrix for a number of benchmark problems. Results demonstrate that improvements in optimality are achieved, especially for maneuvers with large changes in orbital elements. |
| title | Expanding the Class of Quadratic Control-Lyapunov Functions for Low-Thrust Trajectory Optimization |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2408.14412 |